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Different crash tests are carried out in the car industry to measure the acceleration dependent on time. With the aim of improving the airbag-system a discussion of crash processes was raised. Experimental studies approve the modelling of the crash tests as a multifractional Brownian motion which will be introduced as a generalisation of the fractional case (including the Wiener process). Based on the ideas of Coeurjolly [1] an estimation of the significant time-dependent Hurst parameter H(t) will be developed. Its interpretation as a measure of deformation of the crash car leads to interesting results. So the Hurst index’ value is important for supporting the fire-decision [4].

Mathematics Subject Classification (2010): 60H05, 60H30, 62P30.

Keywords: Multifractional Brownian motion, Itô integral, Hurst index,vehicle crash tests, airbag-control-model.